ALABAMA — Lawmakers in Alabama are pushing for rules that would criminalize student speech that mocks or intimidates another student or school employees on social media.

Sen. Arthur Orr introduced a bill on March 3 that would make it a crime if a student posts personal, private or sexual information on social media with the intent to “intimidate or torment” another student or school employee. The law would punish students for all statements — “whether true or false” — that are likely to provoke the stalking or harassment of a student or employee.

The bill would also prohibit students from creating fake social media accounts of other students or school employees and would require school employees to report to police any incidents of cyberbullying.

Orr did not respond to an email or telephone calls requesting comment.

Ronald Krotoszynski, a law professor at the University of Alabama specializing in First Amendment law, said the bill’s “under-inclusive and over-broad” language, which would punish only K-12 students at public and private schools, could “run a real risk of a constitutional problem.”

“You really need to limit laws of this sort to bad behavior that would rise to the level of harassment or assault,” Krotoszynski said. “The law as drafted doesn’t seem to be written with sufficient precision.”

Krotoszynski said the bill’s use of the word “torment” as a standard is problematic because it lacks a legal definition and is a subjective term reliant on the reaction of the speech’s subject.

Krotoszynski said certain provisions of the law, such as criminalizing false speech and hacking into social media accounts, are constitutional. But the provision criminalizing true speech could stop students from speaking about matters of public interest.

“For example, we’ve had several public teachers recently accused of inappropriate sexual conduct with their students,” he said. “Suppose a student wanted to post or repost something from the Birmingham News about his teacher. That would arguably fall within the scope of the prohibition.”

Krotoszynski said the bill could also be used to punish student journalists who write critically of school administrators, even if what they report is true, adding that it could have a chilling effect on student journalism.

More than a dozen states have laws criminalizing cyberbullying, and several states have laws against creating fake social media accounts. A North Carolina law, similar to the Alabama bill, targets students’ speech and makes it illegal to create a social media account in the name of a school employee or otherwise “torment” a school employee online.

In 2011, a high school student challenged a New York law criminalizing cyberbullying after police punished him for posting to his Facebook page pictures of classmates with derogatory sexual comments. In July 2014, the New York State Court of Appeals ruled the law violated the First Amendment because its broad language could criminalize constitutionally protected speech.